To determine how many bonds Setrakian Industries must sell, we first need to calculate the price of a single bond. Then, we will divide the total amount of funds needed ($48.5 million) by the price of one bond.

Here are the key details provided:

• Coupon rate: 5.56% (annual, but paid semiannually)
• YTM (Yield to Maturity): 6.13% (semiannual)
• Maturity: 10 years
• Par value: $2,000
• Total funds needed: $48.5 million

Step 1: Semiannual Coupon Payment

The annual coupon payment is calculated as a percentage of the par value: $\text{Annual Coupon Payment} = 0.0556 \times 2,000 = 111.20$ Since coupons are paid semiannually, the semiannual coupon payment is: $\text{Semiannual Coupon Payment} = \frac{111.20}{2} = 55.60$

Step 2: Number of Periods and YTM per Period

Since the bond pays interest semiannually and matures in 10 years, the number of periods (semiannual periods) is: $N = 10 \times 2 = 20 \text{ periods}$ The semiannual yield (YTM per period) is half of the annual YTM: $\text{Semiannual YTM} = \frac{6.13\%}{2} = 3.065\%$

Step 3: Bond Price Formula

The price of a bond is the present value of the coupon payments and the present value of the face value (par value). The formula is: $\text{Price} = \sum_{t=1}^{N} \frac{\text{Coupon Payment}}{(1 + r)^t} + \frac{\text{Par Value}}{(1 + r)^N}$ Where:

• $N = 20$
• $r = 0.03065$
• Coupon Payment = $55.60
• Par Value = $2,000

We can now calculate this price. Let me compute this.The price of one bond is approximately $1,915.71.

Step 4: Calculate the Number of Bonds to be Sold

To raise $48.5 million, the company needs to sell: $\text{Number of Bonds} = \frac{48,500,000}{1,915.71} \approx 25,317 \text{ bonds}$

Thus, the correct answer is 25,317 bonds.

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Would you like further details or clarification on any step?

Here are some related questions:

1. How would the bond price change if the coupon rate were higher?
2. How does a longer time to maturity affect the bond price?
3. What would happen to the number of bonds needed if the YTM increased?
4. How are the semiannual and annual YTMs related in bond pricing?
5. How is bond duration related to its price sensitivity?

Tip: Bond prices and yields are inversely related: as yields increase, bond prices decrease, and vice versa.